The Mathematical Institute, University of Oxford, Eprints Archive

GMRES for the differentiation operator

Olver, Sheehan (2008) GMRES for the differentiation operator. Technical Report. Unspecified. (Submitted)

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Abstract

We investigate using the GMRES method with the differentiation operator. This operator is unbounded, and thus does not fall into the framework of existing Krylov subspace theory. We establish conditions under which a function can be approximated by its own derivatives in a domain of the complex plane. These conditions are used to determine when GMRES converges. This algorithm outperforms traditional quadrature schemes for a large class of highly oscillatory integrals, even when the kernel of oscillations is unknown.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1074
Deposited By:Lotti Ekert
Deposited On:06 May 2011 08:23
Last Modified:06 May 2011 08:23

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